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Banetta L, Leone F, Anzivino C, Murillo MS, Zaccone A. Microscopic theory for the pair correlation function of liquidlike colloidal suspensions under shear flow. Phys Rev E 2022; 106:044610. [PMID: 36397599 DOI: 10.1103/physreve.106.044610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Accepted: 10/10/2022] [Indexed: 06/16/2023]
Abstract
We present a theoretical framework to investigate the microscopic structure of concentrated hard-sphere colloidal suspensions under strong shear flows by fully taking into account the boundary-layer structure of convective diffusion. We solve the pair Smoluchowski equation with shear separately in the compressing and extensional sectors of the solid angle, by means of matched asymptotics. A proper, albeit approximate, treatment of the hydrodynamic interactions in the different sectors allows us to construct a potential of mean force containing the effect of the flow field on pair correlations. We insert the obtained pair potential in the Percus-Yevick relation and use the latter as a closure to solve the Ornstein-Zernike integral equation. For a wide range of either the packing fraction η and the Péclet (Pe) number, we compute the pair correlation function and extract scaling laws for its value at contact. For all the considered values of Pe, we observe a very good agreement between theoretical findings and numerical results from the literature, up to rather large values of η. The theory predicts a consistent enhancement of the structure factor S(k) at k→0, upon increasing the Pe number. We argue this behavior may signal the onset of a phase transition from the isotropic phase to a nonuniform one, induced by the external shear flow.
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Affiliation(s)
- Luca Banetta
- Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
| | - Francesco Leone
- Department of Physics "A. Pontremoli," University of Milan, via Celoria 16, 20133 Milan, Italy
| | - Carmine Anzivino
- Department of Physics "A. Pontremoli," University of Milan, via Celoria 16, 20133 Milan, Italy
| | - Michael S Murillo
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - Alessio Zaccone
- Department of Physics "A. Pontremoli," University of Milan, via Celoria 16, 20133 Milan, Italy
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2
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Pihlajamaa I, de Bruijn R, van der Schoot P. Geometric percolation of hard-sphere dispersions in shear flow. SOFT MATTER 2022; 18:4167-4177. [PMID: 35593227 PMCID: PMC9157507 DOI: 10.1039/d2sm00375a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Accepted: 05/16/2022] [Indexed: 06/15/2023]
Abstract
We combine a heuristic theory of geometric percolation and the Smoluchowski theory of colloid dynamics to predict the impact of shear flow on the percolation threshold of hard spherical colloidal particles, and verify our findings by means of molecular dynamics simulations. It appears that the impact of shear flow is subtle and highly non-trivial, even in the absence of hydrodynamic interactions between the particles. The presence of shear flow can both increase and decrease the percolation threshold, depending on the criterion used for determining whether or not two particles are connected and on the Péclet number. Our approach opens up a route to quantitatively predict the percolation threshold in nanocomposite materials that, as a rule, are produced under non-equilibrium conditions, making comparison with equilibrium percolation theory tenuous. Our theory can be adapted straightforwardly for application in other types of flow field, and particles of different shape or interacting via other than hard-core potentials.
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Affiliation(s)
- Ilian Pihlajamaa
- Group of Soft Matter and Biological Physics, Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands.
| | - René de Bruijn
- Group of Soft Matter and Biological Physics, Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands.
| | - Paul van der Schoot
- Group of Soft Matter and Biological Physics, Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands.
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Riva S, Banetta L, Zaccone A. Solution to the two-body Smoluchowski equation with shear flow for charge-stabilized colloids at low to moderate Péclet numbers. Phys Rev E 2022; 105:054606. [PMID: 35706254 DOI: 10.1103/physreve.105.054606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2022] [Accepted: 05/05/2022] [Indexed: 06/15/2023]
Abstract
We developed an analytical theoretical method to determine the microscopical structure of weakly to moderately sheared colloidal suspensions in dilute conditions. The microstructure is described by the static structure factor, obtained by solving the stationary two-body Smoluchowski advection-diffusion equation. The singularly perturbed partial differential equation problem is solved by performing an angular averaging over the extensional and compressing sectors and by the rigorous application of boundary-layer theory (intermediate asymptotics). This allows us to expand the solution to a higher order in Péclet with respect to previous methods. The scheme is independent of the type of interaction potential. We apply it to the example of charge-stabilized colloidal particles interacting via the repulsive Yukawa potential and study the distortion of the structure factor. It is predicted that the distortion is larger at small wave vectors k and its dependence on Pe is a simple power law. At increasing Pe, the main peak of the structure factor displays a broadening and shift toward lower k in the extensional sectors, which indicates shear-induced spreading out of particle correlations and neighbor particles locally being dragged away from the reference one. In the compressing sectors, instead, a narrowing and shift toward high k is predicted, reflecting shear-induced ordering near contact and concomitant depletion in the medium range. An overall narrowing of the peak is also predicted for the structure factor averaged over the whole solid angle. Calculations are also performed for hard spheres, showing good overall agreement with experimental data. It is also shown that the shear-induced structure factor distortion is orders of magnitude larger for the Yukawa repulsion than for the hard spheres.
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Affiliation(s)
- Simone Riva
- Department of Physics, A. Pontremoli, University of Milan, Via Celoria 16, 20133 Milan, Italy
| | - Luca Banetta
- Department of Applied Science and Technology (DISAT), Politecnico of Turin, Italy
| | - Alessio Zaccone
- Department of Physics, A. Pontremoli, University of Milan, Via Celoria 16, 20133 Milan, Italy
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB30HE Cambridge, United Kingdom
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Kushnir D, Beyer N, Bartsch E, Hébraud P. Wide-angle static and dynamic light scattering under shear. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2021; 92:025113. [PMID: 33648051 DOI: 10.1063/5.0029533] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2020] [Accepted: 01/26/2021] [Indexed: 06/12/2023]
Abstract
We develop and characterize a wide angle static and dynamic light scattering under shear setup. The apparatus is suitable for the study of the structure and the dynamics of soft materials systems with a sub-micron characteristic length scale. The shear device consists in two parallel plates, and the optical setup allows us to perform light scattering measurements in any plane that contains the gradient of the velocity field direction. We demonstrate several capabilities of our apparatus: a measurement of the evolution with shear of the first peak of the structure factor of a concentrated suspension of spherical particles, both in the compression and extension quadrants of the shear flow, and the measurement of the velocity profile in dynamic light scattering. We present a theoretical treatment of light scattering under flow that takes into account the Gaussian character of the illumination and detection optical paths, in the case where the scattering volume extension is smaller than the gap of the flow cell, and compare with experimental measurements.
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Affiliation(s)
- D Kushnir
- IPCMS, CNRS, Université de Strasbourg 23 rue du Loess 67034 Strasbourg, France
| | - N Beyer
- IPCMS, CNRS, Université de Strasbourg 23 rue du Loess 67034 Strasbourg, France
| | - E Bartsch
- Institut fur Makromolekulare Chemie, Albert-Ludwigs-Universitat Freiburg, Stefan-Meier Straße 31, 79104 Freiburg, Germany
| | - P Hébraud
- IPCMS, CNRS, Université de Strasbourg 23 rue du Loess 67034 Strasbourg, France
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Banetta L, Zaccone A. Radial distribution function of Lennard-Jones fluids in shear flows from intermediate asymptotics. Phys Rev E 2019; 99:052606. [PMID: 31212460 DOI: 10.1103/physreve.99.052606] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2019] [Indexed: 06/09/2023]
Abstract
Determining the microstructure of colloidal suspensions under shear flows has been a challenge for theoretical and computational methods due to the singularly perturbed boundary-layer nature of the problem. Previous approaches have been limited to the case of hard-sphere systems and suffer from various limitations in their applicability. We present an alternative analytic scheme based on intermediate asymptotics which solves the Smoluchowski diffusion-convection equation including both intermolecular and hydrodynamic interactions. The method is able to recover previous results for the hard-sphere fluid and to predict the radial distribution function (rdf) of attractive fluids such as the Lennard-Jones (LJ) fluid. In particular, a new depletion effect is predicted in the rdf of the LJ fluid under shear. This method can be used for the theoretical modeling and understanding of real fluids subjected to flow, with applications ranging from chemical systems to colloids, rheology, plasmas, and atmospherical science.
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Affiliation(s)
- Luca Banetta
- Statistical Physics Group, Department of Chemical Engineering and Biotechnology, University of Cambridge, Cambridge, CB3 0AS, United Kingdom
| | - Alessio Zaccone
- Statistical Physics Group, Department of Chemical Engineering and Biotechnology, University of Cambridge, Cambridge, CB3 0AS, United Kingdom
- Department of Physics "A. Pontremoli", University of Milan, via Celoria 16, 20133 Milan, Italy
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE United Kindgdom
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Wang Z, Iwashita T, Porcar L, Wang Y, Liu Y, Sánchez-Díaz LE, Wu B, Huang GR, Egami T, Chen WR. Local elasticity in nonlinear rheology of interacting colloidal glasses revealed by neutron scattering and rheometry. Phys Chem Chem Phys 2018; 21:38-45. [PMID: 30283930 DOI: 10.1039/c8cp05247f] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The flow of colloidal suspensions is ubiquitous in nature and industry. Colloidal suspensions exhibit a wide range of rheological behavior, which should be closely related to the microscopic structure of the systems. With in situ small-angle neutron scattering complemented by rheological measurements, we investigated the deformation behavior of a charge-stabilized colloidal glass at particle level undergoing steady shear. A short-lived, localized elastic response at particle level, termed as the transient elasticity zone (TEZ), was identified from the neutron spectra. The existence of the TEZ, which could be promoted by the electrostatic interparticle potential, is a signature of deformation heterogeneity: the body of fluids under shear behaves like an elastic solid within the spatial range of the TEZ but like fluid outside the TEZ. The size of the TEZ shrinks as the shear rate increases in the shear thinning region, which shows that the shear thinning is accompanied by a diminishing deformation heterogeneity. More interestingly, the TEZ is found to be the structural unit that provides the resistance to the imposed shear, as evidenced by the quantitative agreement between the local elastic stress sustained by the TEZ and the macroscopic stress from rheological measurements at low and moderate shear rates. Our findings provide an understanding on the nonlinear rheology of interacting colloidal glasses from a micro-mechanical view.
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Affiliation(s)
- Zhe Wang
- Department of Engineering Physics, Tsinghua University, Beijing 100084, China.
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Ingebrigtsen TS, Tanaka H. Structural predictor for nonlinear sheared dynamics in simple glass-forming liquids. Proc Natl Acad Sci U S A 2018; 115:87-92. [PMID: 29247052 PMCID: PMC5776798 DOI: 10.1073/pnas.1711655115] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Glass-forming liquids subjected to sufficiently strong shear universally exhibit striking nonlinear behavior; for example, a power-law decrease of the viscosity with increasing shear rate. This phenomenon has attracted considerable attention over the years from both fundamental and applicational viewpoints. However, the out-of-equilibrium and nonlinear nature of sheared fluids have made theoretical understanding of this phenomenon very challenging and thus slower to progress. We find here that the structural relaxation time as a function of the two-body excess entropy, calculated for the extensional axis of the shear flow, collapses onto the corresponding equilibrium curve for a wide range of pair potentials ranging from harsh repulsive to soft and finite. This two-body excess entropy collapse provides a powerful approach to predicting the dynamics of nonequilibrium liquids from their equilibrium counterparts. Furthermore, the two-body excess entropy scaling suggests that sheared dynamics is controlled purely by the liquid structure captured in the form of the two-body excess entropy along the extensional direction, shedding light on the perplexing mechanism behind shear thinning.
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Affiliation(s)
- Trond S Ingebrigtsen
- Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan
| | - Hajime Tanaka
- Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan
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Huang GR, Wu B, Wang Y, Chen WR. Characterization of microscopic deformation through two-point spatial correlation functions. Phys Rev E 2018; 97:012605. [PMID: 29448320 DOI: 10.1103/physreve.97.012605] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2017] [Indexed: 06/08/2023]
Abstract
The molecular rearrangements of most fluids under flow and deformation do not directly follow the macroscopic strain field. In this work, we describe a phenomenological method for characterizing such nonaffine deformation via the anisotropic pair distribution function (PDF). We demonstrate how the microscopic strain can be calculated in both simple shear and uniaxial extension, by perturbation expansion of anisotropic PDF in terms of real spherical harmonics. Our results, given in the real as well as the reciprocal space, can be applied in spectrum analysis of small-angle scattering experiments and nonequilibrium molecular dynamics simulations of soft matter under flow.
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Affiliation(s)
- Guan-Rong Huang
- Physics Division, National Center for Theoretical Sciences, Hsinchu 30013, Taiwan
- Shull Wollan Center, University of Tennessee and Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Bin Wu
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Yangyang Wang
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Wei-Ren Chen
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Jülich Center for Neutron Science, Forschungszentrum Jülich GmbH, Outstation at SNS, Oak Ridge, Tennessee 37831, USA
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Hess S. Nichtgleichgewichts-Molekulardynamik: Computer-Simulationen von Transportprozessen und Analyse der Struktur von einfachen Fluiden. ACTA ACUST UNITED AC 2013. [DOI: 10.1002/phbl.19880440803] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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10
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Brader JM. Nonlinear rheology of colloidal dispersions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:363101. [PMID: 21386516 DOI: 10.1088/0953-8984/22/36/363101] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
Colloidal dispersions are commonly encountered in everyday life and represent an important class of complex fluid. Of particular significance for many commercial products and industrial processes is the ability to control and manipulate the macroscopic flow response of a dispersion by tuning the microscopic interactions between the constituents. An important step towards attaining this goal is the development of robust theoretical methods for predicting from first-principles the rheology and nonequilibrium microstructure of well defined model systems subject to external flow. In this review we give an overview of some promising theoretical approaches and the phenomena they seek to describe, focusing, for simplicity, on systems for which the colloidal particles interact via strongly repulsive, spherically symmetric interactions. In presenting the various theories, we will consider first low volume fraction systems, for which a number of exact results may be derived, before moving on to consider the intermediate and high volume fraction states which present both the most interesting physics and the most demanding technical challenges. In the high volume fraction regime particular emphasis will be given to the rheology of dynamically arrested states.
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Affiliation(s)
- J M Brader
- Fachbereich Physik, Universit¨at Konstanz, D-78457 Konstanz, Germany
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11
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Hess S, Loose W. Flow Properties and Shear-induced Structural Changes in Fluids: A Case Study on the Interplay between Theory, Simulation, Experiment and Application. ACTA ACUST UNITED AC 2010. [DOI: 10.1002/bbpc.19900940304] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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12
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Lenstra TA, Dhont JK. Flow dichroism in critical colloidal fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:061401. [PMID: 11415098 DOI: 10.1103/physreve.63.061401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2000] [Revised: 10/01/2000] [Indexed: 05/23/2023]
Abstract
Due to long-range correlations and slow dynamics of concentration fluctuations in the vicinity of the gas-liquid critical point, shear flow is very effective in distorting the microstructure of near-critical fluids. The anisotropic nature of the shear-field renders the microstructure highly anisotropic, leading to dichroism. Experiments on the dichroic behavior can thus be used to test theoretical predictions on microstructural order under shear flow conditions. We performed both static and dynamic dichroism and turbidity measurements on a colloid-polymer mixture, existing of silica spheres (radius 51 nm) and polydimethylsiloxane polymer (molar weight 204 kg/mol). Sufficiently far away from the critical point, in the mean-field region, the experimental data are in good agreement with theory. Very close to the critical point, beyond mean field, for which no theory exists yet, an unexpected decrease of dichroism on approach of the critical point is observed. Moreover, we do not observe critical slowing down of shear-induced dichroism, right up to the critical point, in contrast to the turbidity.
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Affiliation(s)
- T A Lenstra
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands
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13
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Szamel G. Nonequilibrium structure and rheology of concentrated colloidal suspensions: Linear response. J Chem Phys 2001. [DOI: 10.1063/1.1366335] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Vermant J, Raynaud L, Mewis J, Ernst B, Fuller GG. Large-Scale Bundle Ordering in Sterically Stabilized Latices. J Colloid Interface Sci 1999; 211:221-229. [PMID: 10049538 DOI: 10.1006/jcis.1998.6008] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Time-resolved small-angle light scattering and linear conservative dichroism measurements are presented for concentrated, sterically stabilized, aqueous latices under simple shear flow. At low stress levels, flow causes a mild distortion of the liquid-like structure in colloidally stable dispersions, which is quite well understood. In this paper flow-induced structures are investigated in concentrated dispersions when the system is brought far from equilibrium by means of hydrodynamic forces. At high stress levels various structural changes have been predicted by numerical simulation, among others string phases oriented in the flow direction. Here, experimental results are reported on a bundle-like ordering in very dense systems, which involves a length scale much larger than that of a single string of particles. Two latices, with different particle sizes and different thicknesses of the stabilizing layer, are compared. The occurrence of the bundle-like ordering is related to the rheological behavior: it causes a significant decrease in viscosity. It is shown that the presence of this phase results in a structural hysteresis, which explains a thixotropic behavior that is encountered in some stable colloidal suspensions. Also the relaxation behavior of the bundle-like phases has been studied. Interparticle forces are found to have a very strong effect on the relaxation time scales. Copyright 1999 Academic Press.
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Affiliation(s)
- J Vermant
- Department of Chemical Engineering, K. U. Leuven, de Croylaan 46, Heverlee, B-3001, Belgium
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Morin B, Ronis D. Disorder and order in sheared colloidal suspensions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:576-587. [PMID: 9965102 DOI: 10.1103/physreve.54.576] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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16
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Dhont JKG, Verduin H. The effect of shear‐flow on critical correlations in colloidal systems: Microstructure, turbidity, and dichroism. J Chem Phys 1994. [DOI: 10.1063/1.468401] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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17
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Blawzdziewicz J, Szamel G. Structure and rheology of semidilute suspension under shear. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:4632-4636. [PMID: 9961145 DOI: 10.1103/physreve.48.4632] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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18
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Szamel G, Blawzdziewicz J, Leegwater JA. Self-diffusion in sheared suspensions: Violation of the Einstein relation. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:2173-2176. [PMID: 9907233 DOI: 10.1103/physreva.45.r2173] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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19
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de Kruif CG, van der Werff JC, Johnson SJ, May RP. Small‐angle neutron scattering of sheared concentrated dispersions: Microstructure along principal flow axes. ACTA ACUST UNITED AC 1990. [DOI: 10.1063/1.857561] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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20
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Ackerson BJ, De Kruif CG, Wagner NJ, Russel WB. Comparison of small shear flow rate–small wave vector static structure factor data with theory. J Chem Phys 1989. [DOI: 10.1063/1.455877] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Lutsko JF, Dufty JW, Das SP. Fluctuations and dissipation in a fluid under shear: Linear dynamics. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 39:1311-1324. [PMID: 9901368 DOI: 10.1103/physreva.39.1311] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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22
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Johnson SJ, de Kruif CG, May RP. Structure factor distortion for hard‐sphere dispersions subjected to weak shear flow: Small‐angle neutron scattering in the flow–vorticity plane. J Chem Phys 1988. [DOI: 10.1063/1.455542] [Citation(s) in RCA: 45] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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23
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Ackerson BJ, Pusey PN. Shear-induced order in suspensions of hard spheres. PHYSICAL REVIEW LETTERS 1988; 61:1033-1036. [PMID: 10039497 DOI: 10.1103/physrevlett.61.1033] [Citation(s) in RCA: 99] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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24
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Ackerson BJ. Hard-sphere dispersions: Small-wave-vector structure-factor measurements in a linear shear flow. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 37:4819-4827. [PMID: 9899629 DOI: 10.1103/physreva.37.4819] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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25
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Hanley HJ, Rainwater JC, Hess S. Shear-induced angular dependence of the liquid pair correlation function. PHYSICAL REVIEW. A, GENERAL PHYSICS 1987; 36:1795-1802. [PMID: 9899060 DOI: 10.1103/physreva.36.1795] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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26
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Kalus J, Hoffman H. Nearest neighbor order in an aligned solution of interacting rod‐like micelles. J Chem Phys 1987. [DOI: 10.1063/1.453568] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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